以下是两种基本的蚁群优化（ACO）算法实现方式，分别使用了邻接矩阵和邻接表来表示图，代码示例如下：

1. 使用邻接矩阵实现：

import numpy as np

# 创建邻接矩阵
adj_matrix = np.array([[0, 1, 0, 0],
                       [1, 0, 1, 1],
                       [0, 1, 0, 1],
                       [0, 1, 1, 0]])

# 初始化信息素矩阵
pheromone_matrix = np.ones(adj_matrix.shape) * 0.1

# ACO算法主要步骤
def aco(adj_matrix, pheromone_matrix, num_ants, num_iterations):
    num_nodes = adj_matrix.shape[0]
    best_path = None
    best_cost = float('inf')

    for iteration in range(num_iterations):
        # 每只蚂蚁都从起点开始
        ant_current_node = np.zeros(num_ants, dtype=int)

        path = np.zeros((num_ants, num_nodes), dtype=int)
        path_costs = np.zeros(num_ants)

        for step in range(num_nodes - 1):
            for ant in range(num_ants):
                # 计算蚂蚁的下一步
                valid_nodes = np.arange(num_nodes)[adj_matrix[ant_current_node[ant]] != 0]
                probabilities = pheromone_matrix[ant_current_node[ant]][valid_nodes] ** alpha * (1.0 / adj_matrix[ant_current_node[ant]][valid_nodes]) ** beta
                probabilities = probabilities / np.sum(probabilities)
                next_node = np.random.choice(valid_nodes, p=probabilities)

                # 更新路径和路径成本
                path[ant, step] = ant_current_node[ant]
                path_costs[ant] += adj_matrix[ant_current_node[ant]][next_node]
                ant_current_node[ant] = next_node

        # 完成路径
        for ant in range(num_ants):
            path[ant, -1] = ant_current_node[ant]
            path_costs[ant] += adj_matrix[ant_current_node[ant]][0]

        # 更新最优路径
        best_ant = np.argmin(path_costs)
        if path_costs[best_ant] < best_cost:
            best_path = path[best_ant]
            best_cost = path_costs[best_ant]

        # 更新信息素矩阵
        delta_pheromone = np.zeros(adj_matrix.shape)
        for ant in range(num_ants):
            for i in range(num_nodes - 1):
                delta_pheromone[path[ant, i]][path[ant, i + 1]] += Q / path_costs[ant]

        pheromone_matrix = (1 - rho) * pheromone_matrix + delta_pheromone

    return best_path, best_cost

# 参数设置
num_ants = 10
num_iterations = 100
alpha = 1.0
beta = 2.0
rho = 0.5
Q = 1.0

# 运行ACO算法
best_path, best_cost = aco(adj_matrix, pheromone_matrix, num_ants, num_iterations)

print("最优路径：", best_path)
print("最优成本：", best_cost)

2. 使用邻接表实现：

from collections import defaultdict

# 创建邻接表
adj_list = defaultdict(list)
adj_list[0] = [1]
adj_list[1] = [0, 2, 3]
adj_list[2] = [1, 3]
adj_list[3] = [1, 2]

# 初始化信息素矩阵
pheromone_matrix = defaultdict(lambda: defaultdict(lambda: 0.1))

# ACO算法主要步骤
def aco(adj_list, pheromone_matrix, num_ants, num_iterations):
    num_nodes = len(adj_list)
    best_path = None
    best_cost = float('inf')

    for iteration in range(num_iterations):
        # 每只蚂蚁都从起点开始
        ant_current_node = [0] * num_ants

        path = [[0] * num_nodes for _ in range(num_ants)]
        path_costs = [0] * num_ants

        for step in range